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Author: Tinku Tara

Question-130369

Question Number 130369 by gowsalya last updated on 24/Jan/21 Answered by Olaf last updated on 24/Jan/21 $$\Omega\:=\:\int_{\mid{z}\mid=\mathrm{1}} {xdz} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{cos}\theta{d}\left(\mathrm{cos}\theta+{i}\mathrm{sin}\theta\right) \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi}…

f-x-2x-1-x-2-2x-3-Domain-D-f-

Question Number 130362 by greg_ed last updated on 24/Jan/21 $$\mathrm{f}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\mid\mathrm{2}{x}−\mathrm{3}\mid}} \\ $$$$\mathrm{Domain}\:\mathrm{D}_{\mathrm{f}} \:=\:? \\ $$ Answered by ajfour last updated on 24/Jan/21 $${x}^{\mathrm{2}} >\mid\mathrm{2}{x}−\mathrm{3}\mid…

f-x-4x-2-1-2x-2-1-prove-that-1-f-x-2-

Question Number 130354 by greg_ed last updated on 24/Jan/21 $$\mathrm{f}\left({x}\right)=\frac{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{1}\:\leqslant\:\mathrm{f}\left({x}\right)\:\leqslant\:\mathrm{2} \\ $$ Answered by MJS_new last updated on 24/Jan/21 $${f}\left({x}\right)=\mathrm{2}−\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}}…

find-dx-1-cosx-cos-2x-

Question Number 64818 by mathmax by abdo last updated on 22/Jul/19 $${find}\:\int\:\:\:\frac{{dx}}{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)} \\ $$ Commented by mathmax by abdo last updated on 22/Jul/19 $${let}\:{I}\:=\int\:\frac{{dx}}{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)}\:\Rightarrow\:{I}\:=\int\:\frac{{dx}}{\mathrm{1}+{cosx}+\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}}…